Advertisements
Advertisements
प्रश्न
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
पर्याय
90,000
10,000
30,240
69,760
उत्तर
The number of 5-digit telephone numbers having atleast one of their digits repeated is 69,760.
Explanation:
Total number of 5-digit telephone number if all the digits are repeated = (10)5 ......[∵ Digits are from 0 to 9]
If digits are not repeated, then 5-digit telephones, can be formed in 10P5 ways
∴ Required number of ways = (10)5 – 10P5
= `100000 - (10!)/((10 - 5)!)`
= `100000 - (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5!)`
= 100000 – 30240
= 69760
APPEARS IN
संबंधित प्रश्न
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
The number of ways to arrange the letters of the word CHEESE are
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
